fun fact
signatures are now called witnesses
segregating them is actually one of the features segwit enabled nodes can offer
they even have 2 txid's and merkle trees for exactly this function
(it really does pay to read some code and understand the word "segretated witness")
yes
unupgraded nodes that do not understand segwit will have a stripped block not containing the witness(signatures)
(the stripped blocks are filtered to non-segwit nodes from a segwit enabled node doing the stripping for the non segwit node)
it required alot of cludgy code to do this "backward compatible " data striping feature, where it required segwit enabled nodes to do the stripping if they had unupgraded peers connected to them.
pushing the unupgraded peers to the outer hops of the relay network where they dont get to be the normal class of nodes validating everything
..
oh and NO one said all blocks dont have signatures any more. NO one
its just another misdirection social game.
the actual debates were that non segwit nodes lost their "full node status" by being handled differently given a different lump of data than a segwit enabled node got